Direct effects on the membrane potential due to "pumps" that transfer no net charge

The effects of active ionic transport are included in the derivation of a general expression for the zero current membrane potential. It is demonstrated that an active transport system that transfers no net charge (nonrheogenic) may, nevertheless, directly alter the membrane potential. This effect depends upon the exchange of matter within the membrane between the active and passive diffusion regimes. Furthermore, in the presence of such exchange, the transmembrane active fluxes measured by the usual techniques and the local pumped fluxes are not identical. Several common uses of the term “electrogenic pump” are thus shown to be inconsistent with each other. These inconsistencies persist when the derivation is extended to produce a Goldman equation modified to account for active transport; however, that equation is shown to be limited by less narrow constraints on membrane heterogeneity and internal electric field than those previously required. In particular, it is applicable to idealized mosaic membranes limited by these requirements.     

The independence principle. A reconsideration

The electrodiffusion model presented in the previous paper, which specifically excludes ion-ion interactions, is analyzed for the ratio of one-way fluxes (flux ratio) as a function of the ionic driving force across the membrane. Significant deviations from the behavior expected on the basis of the Ussing relation are found. These are sufficient to explain the “nonindependent” ion movement noted in some biological flux ratio data. One-way fluxes are dependent on the ionic concentration on both sides of the membrane. The coupling of these fluxes to ionic concentrations comes from the dependence of ionic mobility and the diffusion coefficient on the equilibrium potential. It is concluded that nonindependent behavior in experimental data is not sufficient to implicate ion-ion interaction as the source of the discrepancy.     

Deviations from the flux ratio equation for chloride ions in ouabain- and acetazolamide-treated frog skin

In order to establish whether or not chloride ions behave as freely moving particles in “passive”, i.e. ouabain-and acetazolamide-treated, frog skin, tracer fluxes of ³⁶Cl⁻ have been measured while a voltage (generally +40 mV, serosal side positive) across the skin was applied. Ussing's flux ratio equation has been used as a criterion for this type of transport. One group of skin samples exhibited significant exchange diffusion phenomena. Most samples in a second group either behaved according to the flux ratio equation or showed significant and extreme exchange diffusion. From flux ratios obtained at two different voltages across various skin samples, showing extreme exchange diffusion, it appeared that the simple form of Kedem and Essig's law derived from irreversible thermodynamics, which is valid for homogeneous systems, does not apply to the type of exchange diffusion found. The system can, however, be described by a 1 : 1 exchange mechanism working in parallel with a diffusional pathway. The ratio exchange flux/observed efflux must then have a constant value (0.83) at the voltages applied, which implies that the exchange flux is voltage dependent. By comparison with iodide flux experiments as carried out by Ussing, it is shown that iodide exhibits the same type of exchange diffusion. A carrier, possibly responsibe for the observed behaviour, is described.     

Equivalent Circuits as Related to Ionic Systems

The purpose of this paper is to clarify the relationship between certain “equivalent circuits” and the fundamental flux equations of Nernst and Planck. It is shown that as a direct algebraic consequence of these equations one may construct two types of equivalent circuits for a homogeneous (charged or uncharged) membrane. The one, which we term the “pure electrical equivalent circuit,” correctly predicts all of the electrical properties of the membrane for both steady and transient states. The other, which we call the “mixed equivalent circuit,” predicts the steady state I, Ψ characteristics of the membrane and the steady state ionic fluxes; it is not applicable to non-steady state properties or measurements. We emphasize that with regard to the portrayal of the physical basis of the properties of a homogeneous membrane, the mixed equivalent circuit can be misleading. This is particularly significant because this same circuit can also be used to depict a mosaic membrane, in which case the circuit gives a realistic pictorialization of the physical origin of the membrane properties. It is hoped that our analysis will be of aid to workers in electrophysiology who make use of equivalent circuit terminology in discussing the behavior of the plasma membrane.     

A quantitative analysis of the voltage-current relationships of fixed charge membranes and the associated property of "punch-through"

A theoretical analysis of the voltage-current relationship is carried out in a membrane consisting of two fixed charge regions, of opposite sign, in contact. This is achieved by applying the diffusion equations to this system in conjunction with the Poisson-Boltzmann equation. The latter has been successfully applied by Mauro to determine the profiles of the electrostatic potential in his treatment of the capacitative property of such a system. It is shown that the system displays the property of rectification and is very similar in many respects to a solid state P-N junction diode. It is also shown that for the case of reverse bias, an electrical breakdown phenomena can occur. This is referred to as the “punch-through” effect. “Punch-through” was observed in experiments on the electrical characteristics of the membranes of Chara australis and Nitella sp. The experimental results are discussed in relation to the theoretical analysis.     

The Intracellular Transport and Distribution of Cysteamine Phosphate Derivatives

Radioautography and extractive techniques were used to analyze the transport of cysteamine phosphate and its derivatives in salamander oocytes. The quantitative relations among the processes involved — membrane permeation, enzymatic dephosphorylation, binding through mixed disulfide formation, and cytoplasmic diffusion — were elucidated. Within the detection limits, all of the intracellular material is present as dephosphorylated derivatives. Cytoplasmic diffusion is effectively slowed by binding (the “chromatographic” effect) and makes an appreciable contribution to cellular flux rates. As a consequence, one can observe by radioautography a cortical diffusion ring which spreads inward as a function of influx time, while also increasing in peak density because of the finite membrane permeability. Good agreement was found between the transport parameters determined by radioautography and those from influx data for the whole oocyte. The ratio of nuclear to cytoplasmic concentrations of the cysteamine phosphate derivatives at equilibrium is about 0.4. The nuclear membrane is, however, a negligible barrier to transport, and the asymmetry appears to arise primarily from the quantity and sulfhydryl content of the binding proteins in the two compartments.     

The Double Fixed Charge Membrane: Solution-Membrane Ion Partition Effects and Membrane Potentials

An analysis is made of the effect of solution-membrane partition of ions on the electrostatic potential and ion concentration profiles in fixed charge membranes. It is shown that the inclusion of partition effects gives rise to large solution-membrane “Donnan” potentials even when the concentration of fixed charges is of the same order as the concentration of the external solution. This effect renders the system and the simplified analysis of the double fixed charge membrane (FCM) previously given more applicable to biological membranes. An analysis is also given of the voltage dependence of the fluxes of individual ion species in the double FCM when it separates different ionic solutions and an expression is deduced for the membrane resting potential. Although the latter is similar in form to the Goldman-Hodgkin-Katz (GHK) equation the corresponding value of the permeability ratio P_C1/P_K is under certain specified conditions both concentration and potential dependent.     

Membrane Uncoating of Intact Enveloped Viruses

Experiments in the 1960s showed that Sendai virus, a paramyxovirus, fused its membrane with the host plasma membrane. After membrane fusion, the virus spontaneously “uncoated” with diffusion of the viral membrane proteins into the host plasma membrane and a merging of the host and viral membranes. This led to deposit of the viral ribonucleoprotein (RNP) and interior proteins in the cell cytoplasm. Later work showed that the common procedure then used to grow Sendai virus produced damaged, pleomorphic virions. Virions, which were grown under conditions that were not damaging, made a connecting structure between virus and cell at the region where the fusion occurred. The virus did not release its membrane proteins into the host membrane. The viral RNP was seen in the connecting structure in some cases. Uncoating of intact Sendai virus proceeds differently from uncoating described by the current standard model developed long ago with damaged virus. A model of intact paramyxovirus uncoating is presented and compared to what is known about the uncoating of other viruses.Enveloped virus entry at the plasma membrane includes binding of the virion to one or more receptors, changes in the virion components, membrane fusion, and membrane uncoating. The term “membrane uncoating” is being used to describe the separation of internal virion components from the viral membrane so the internal components can enter the cell. The term “uncoating” is sometimes used to mean the release of the viral genome from the capsid or other structures that have also entered the cell, but in this review, the term “membrane uncoating” will be used to represent only the separation of the virion internal contents and the viral envelope.Much of the original model of membrane fusion and uncoating was generally accepted as a result of a 1968 paper by Morgan and Howe (41). That paper provided strong evidence that Sendai virus (a paramyxovirus) entered a cell by fusion of the viral membrane with the cell plasma membrane. After membrane fusion, the virion rapidly lost its structure as the viral membrane merged with the host membrane and its components became part of the host membrane. The viral ribonucleoprotein (RNP) and internal proteins were released into the cytoplasm. This model of membrane uncoating is still generally accepted. For instance, in a 2007 virology text (24), this model was presented and illustrated with a figure from the Morgan and Howe paper. (The same figure is shown here as Fig. 2B.)Later, it was shown that Sendai viruses, which had been grown in fertilized chicken eggs, had different properties depending whether they had been harvested after growth for roughly 1 day (“early harvest”) or for several days (“late harvest”). The early-harvest viruses appear to be intact, but the late-harvest viruses have a different morphology and appear to be damaged (20, 26).This review summarizes data showing that intact early-harvest Sendai viruses uncoat quite differently from the way damaged late-harvest Sendai viruses uncoat. A model of intact paramyxovirus membrane uncoating is presented. The membrane uncoating of some other enveloped viruses that enter at the plasma membrane is compared to that described by this model.     

Anomalous permeabilities of the egg cell membrane of a starfish in K(+)-Tl(+) mixtures

The electrical properties of “inward” rectifying egg cell membranes of the starfish mediastera aequalis have been studied in the presence of K(+)-Tl(+) mixtures. When the ratio of the external concentrations of these ions is changed while their sum is kept constant, both the conductance and the zero-current membrane potential go through a minimum, showing clear discrepancies from theoretical results based on conventional electrodiffusion models (E.g., Goldman’s equation). By contrast, when the ration of the two concentrations is fixed and their sum varied, the potential follows an ideal Nernst slope, consistent with Goldman’s equation. The membrane conductance which, according to previous studies on similar membranes, is to be viewed as a function of the displacement of the membrane potential from its resting value δV, shows marked differences between the cases in which K(+) or Tl(+) are the predominant ions: when K(+) is the predominant permeant ion in solution, the addition of small amounts of Tl(+) inhibits the current, while corresponding blocking effects of K(+) on the current are not observed when Tl(+) is the predominant permeant ion. Also, the time course of the conductance during voltage clamp is different in the two cases, being much faster in Tl(+) than in K(+) solution for comparable values of δV. Most of the above features are accounted for by a model in which it is assumed that the ionic channels have external binding sites for cations and that their permeability properties depend on the species of the cation bound (K(+)or Tl(+) in the present experiments).     

Modelling of Thyroid Peroxidase Reveals Insights into Its Enzyme Function and Autoantigenicity

Thyroid peroxidase (TPO) catalyses the biosynthesis of thyroid hormones and is a major autoantigen in Hashimoto’s disease—the most common organ-specific autoimmune disease. Epitope mapping studies have shown that the autoimmune response to TPO is directed mainly at two surface regions on the molecule: immunodominant regions A and B (IDR-A, and IDR-B). TPO has been a major target for structural studies for over 20 years; however, to date, the structure of TPO remains to be determined. We have used a molecular modelling approach to investigate plausible modes of TPO structure and dimer organisation. Sequence features of the C-terminus are consistent with a coiled-coil dimerization motif that most likely anchors the TPO dimer in the apical membrane of thyroid follicular cells. Two contrasting models of TPO were produced, differing in the orientation and exposure of their active sites relative to the membrane. Both models are equally plausible based upon the known enzymatic function of TPO. The “trans” model places IDR-B on the membrane-facing side of the myeloperoxidase (MPO)-like domain, potentially hindering access of autoantibodies, necessitating considerable conformational change, and perhaps even dissociation of the dimer into monomers. IDR-A spans MPO- and CCP-like domains and is relatively fragmented compared to IDR-B, therefore most likely requiring domain rearrangements in order to coalesce into one compact epitope. Less epitope fragmentation and higher solvent accessibility of the “cis” model favours it slightly over the “trans” model. Here, IDR-B clusters towards the surface of the MPO-like domain facing the thyroid follicular lumen preventing steric hindrance of autoantibodies. However, conformational rearrangements may still be necessary to allow full engagement with autoantibodies, with IDR-B on both models being close to the dimer interface. Taken together, the modelling highlights the need to consider the oligomeric state of TPO, its conformational properties, and its proximity to the membrane, when interpreting epitope-mapping data.     

High membrane permeability for melatonin

The pineal gland, an endocrine organ in the brain, synthesizes and secretes the circulating night hormone melatonin throughout the night. The literature states that this hormone is secreted by simple diffusion across the pinealocyte plasma membrane, but a direct quantitative measurement of membrane permeability has not been made. Experiments were designed to compare the cell membrane permeability to three indoleamines: melatonin and its precursors N-acetylserotonin (NAS) and serotonin (5-HT). The three experimental approaches were (1) to measure the concentration of effluxing indoleamines amperometrically in the bath while cells were being dialyzed internally by a patch pipette, (2) to measure the rise of intracellular indoleamine fluorescence as the compound was perfused in the bath, and (3) to measure the rate of quenching of intracellular fura-2 dye fluorescence as indoleamines were perfused in the bath. These measures showed that permeabilities of melatonin and NAS are high (both are uncharged molecules), whereas that for 5-HT (mostly charged) is much lower. Comparisons were made with predictions of solubility-diffusion theory and compounds of known permeability, and a diffusion model was made to simulate all of the measurements. In short, extracellular melatonin equilibrates with the cytoplasm in 3.5 s, has a membrane permeability of ∼1.7 µm/s, and could not be retained in secretory vesicles. Thus, it and NAS will be “secreted” from pineal cells by membrane diffusion. Circumstances are suggested when 5-HT and possibly catecholamines may also appear in the extracellular space passively by membrane diffusion.     

Femtosecond Optoinjection of Intact Tobacco BY-2 Cells Using a Reconfigurable Photoporation Platform

A tightly-focused ultrashort pulsed laser beam incident upon a cell membrane has previously been shown to transiently increase cell membrane permeability while maintaining the viability of the cell, a technique known as photoporation. This permeability can be used to aid the passage of membrane-impermeable biologically-relevant substances such as dyes, proteins and nucleic acids into the cell. Ultrashort-pulsed lasers have proven to be indispensable for photoporating mammalian cells but they have rarely been applied to plant cells due to their larger sizes and rigid and thick cell walls, which significantly hinders the intracellular delivery of exogenous substances. Here we demonstrate and quantify femtosecond optical injection of membrane impermeable dyes into intact BY-2 tobacco plant cells growing in culture, investigating both optical and biological parameters. Specifically, we show that the long axial extent of a propagation invariant (“diffraction-free”) Bessel beam, which relaxes the requirements for tight focusing on the cell membrane, outperforms a standard Gaussian photoporation beam, achieving up to 70% optoinjection efficiency. Studies on the osmotic effects of culture media show that a hypertonic extracellular medium was found to be necessary to reduce turgor pressure and facilitate molecular entry into the cells.     

PTEN Hopping on the Cell Membrane Is Regulated via a Positively-Charged C2 Domain

PTEN, a tumor suppressor that is frequently mutated in a wide spectrum of cancers, exerts PI(3,4,5)P₃ phosphatase activities that are regulated by its dynamic shuttling between the membrane and cytoplasm. Direct observation of PTEN in the interfacial environment can offer quantitative information about the shuttling dynamics, but remains elusive. Here we show that positively charged residues located in the cα2 helix of the C2 domain are necessary for the membrane localization of PTEN via stable electrostatic interactions in Dictyostelium discoideum. Single-molecule imaging analyses revealed that PTEN molecules moved distances much larger than expected had they been caused by lateral diffusion, a phenomenon we call “hopping.” Our novel single-particle tracking analysis method found that the cα2 helix aids in regulating the hopping and stable-binding states. The dynamically established membrane localization of PTEN was revealed to be essential for developmental processes and clarified a fundamental regulation mechanism of the protein quantity and activity on the plasma membrane.     

The Interaction between Osmotic- and Pressure-induced Water Flow in Plant Roots

This paper presents a general model for coupled solute and water flow through plant roots based on the thermodynamics of irreversible processes. The model explains in a straight-forward manner such experimentally observed phenomena as changes in root resistance, increased solute flux, and apparent negative resistance, which have been reported for root systems under the influence of a hydrostatic pressure gradient. These apparent anomalies are explained on the basis of the interaction between the osmotic and hydrostatic driving forces and the well known “sweeping away” or dilution effect. We show that with a constant hydraulic conductivity the only features necessary to explain these phenomena are some type of membrane or membranelike structure and a mechanism for actively accumulating solutes.     

Membrane voltage as a dynamic platform for spatiotemporal signaling,physiological, and developmental regulation

Membrane voltage arises from the transport of ions through ion-translocating ATPases, ion-coupled transport of solutes, and ion channels, and is an integral part of the bioenergetic “currency” of the membrane. The dynamics of membrane voltage—so-called action, systemic, and variation potentials—have also led to a recognition of their contributions to signal transduction, both within cells and across tissues. Here, we review the origins of our understanding of membrane voltage and its place as a central element in regulating transport and signal transmission. We stress the importance of understanding voltage as a common intermediate that acts both as a driving force for transport—an electrical “substrate”—and as a product of charge flux across the membrane, thereby interconnecting all charge-carrying transport across the membrane. The voltage interconnection is vital to signaling via second messengers that rely on ion flux, including cytosolic free Ca²⁺, H⁺, and the synthesis of reactive oxygen species generated by integral membrane, respiratory burst oxidases. These characteristics inform on the ways in which long-distance voltage signals and voltage oscillations give rise to unique gene expression patterns and influence physiological, developmental, and adaptive responses such as systemic acquired resistance to pathogens and to insect herbivory.

Membrane voltage serves as a platform coordinating ion flux to transmit and transduce biological signals.

Advances

• The biophysics of transport that determine membrane voltage are well-described with quantitative flux equations.
• In the models of the guard cell and the giant algae Chara and Nitella these charge-transporting processes accurately describe and predict physiological behavior, including the coupling of membrane voltage oscillations with ion flux, [Ca²⁺]_i, pH, their consequences for cellular osmotic adjustments, and their spatial propagation.
• Unlike neuronal and other animal tissues, action potentials in plants are mediated by a temporal sequence of ion flux through Ca²⁺ and Cl^- channels with voltage recovery driven by ion flux through K⁺ channels. The interplay of channel-mediated ion flux and changes in H⁺-ATPase activity are likely responsible for the slower propagation of variation and systemic potentials.
• In terrestrial plants, membrane voltage transients may propagate along vascular traces, both through the parenchymal cells lining the xylem and through the phloem. Propagation of such voltage transients is associated with glutamate receptor-like channels that may contribute to plasma membrane Ca²⁺ flux and [Ca²⁺]_i elevations.
• Changes in [Ca²⁺]_i, pH, and reactive oxygen species are key mediators that translate voltage signals into physiological, developmental, and adaptive responses in plant tissues.

     

Deviations from the flux ratio equation for chloride ions in ouabain- and acetazolamide-treated frog skin.

In order to establish whether or not chloride ions behave as freely moving particles in "passive", i.e. ouabain- and acetazolamide-treated, frog skin, tracer fluxes of 36Cl-have been measured while a voltage (generally +40 mV, serosal side positive) across the skin was applied. Ussing's flux ratio equation has been used as a criterion for this type of transport. One group of skin samples exhibited significant exchange diffusion phenomena. Most samples in a second group either behaved according to the flux ratio equation of showed significant and extreme exchange diffusion. From flux ratios obtained at two different voltages across various skin samples, showing extreme exchange diffusion, it appeared that the simple form of Kedem and Essig's law derived from irreversible thermodynamics, which is valid for homogeneous systems, does not apply to the type of exchange diffusion found. The system can, however, be described by a 1:1 exchange mechanism working in parallel with a diffusional pathway. The ratio exchange flux/observed efflux must then have a constant value (0.83) at the voltages appled, which implies that the exchange flux is voltage dependent. By comparison with iodide flux experiments as carried out by Ussing, it is shown that iodide exhibits the same type of exchange diffusion. A carrier, possibly responsible for the observed behaviour, is described.     

Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm

MotivationGenome-scale metabolic networks can be modeled in a constraint-based fashion. Reaction stoichiometry combined with flux capacity constraints determine the space of allowable reaction rates. This space is often large and a central challenge in metabolic modeling is finding the biologically most relevant flux distributions. A widely used method is flux balance analysis (FBA), which optimizes a biologically relevant objective such as growth or ATP production. Although FBA has proven to be highly useful for predicting growth and byproduct secretion, it cannot predict the intracellular fluxes under all environmental conditions. Therefore, alternative strategies have been developed to select flux distributions that are in agreement with experimental “omics” data, or by incorporating experimental flux measurements. The latter, unfortunately can only be applied to a limited set of reactions and is currently not feasible at the genome-scale. On the other hand, it has been observed that micro-organisms favor a suboptimal growth rate, possibly in exchange for a more “flexible” metabolic network. Instead of dedicating the internal network state to an optimal growth rate in one condition, a suboptimal growth rate is used, that allows for an easier switch to other nutrient sources. A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions.ResultsHere, we propose Maximum Metabolic Flexibility (MMF) a computational method that utilizes this observation to find the most probable intracellular flux distributions. By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space. Constraining the selected reactions improves the quantitative predictions of FBA considerably more than adding an equal amount of flux constraints, selected using a more naïve approach. Our method can be applied to any cell type without requiring prior information.AvailabilityMMF is freely available as a MATLAB plugin at: http://cs.ru.nl/~wmegchel/mmf.     

The C-terminal extension of ferrochelatase is critical for enzyme activity and for functioning of the tetrapyrrole pathway in Synechocystis strain PCC 6803

Heme and chlorophyll (Chl) share a common biosynthetic pathway up to the branch point where magnesium chelatase and ferrochelatase (FeCH) insert either magnesium for Chl biosynthesis or ferrous iron for heme biosynthesis. A distinctive feature of FeCHs in cyanobacteria is their C-terminal extension, which forms a putative transmembrane segment containing a Chl-binding motif. We analyzed the ΔH324 strain of Synechocystis sp. strain PCC 6803, which contains a truncated FeCH enzyme lacking this C-terminal domain. Truncated FeCH was localized to the membrane fraction, suggesting that the C-terminal domain is not necessary for membrane association of the enzyme. Measurements of enzyme activity and complementation experiments revealed that the ΔH324 mutation dramatically reduced activity of the FeCH, which resulted in highly upregulated 5-aminolevulinic acid synthesis in the ΔH324 mutant, implying a direct role for heme in the regulation of flux through the pathway. Moreover, the ΔH324 mutant accumulated a large amount of protoporphyrin IX, and levels of Chl precursors were also significantly increased, suggesting that some, but not all, of the “extra” flux can be diverted down the Chl branch. Analysis of the recombinant full-length and truncated FeCHs demonstrated that the C-terminal extension is critical for activity of the FeCH and that it is strictly required for oligomerization of this enzyme. The observed changes in tetrapyrrole trafficking and the role of the C terminus in the functioning of FeCH are discussed.     

Analysis of Permeability Data for the Case of Parallel Diffusion Pathways

A method of analyzing permeability or diffusion temperature-flux data, for the case of two parallel, independent diffusion fluxes is presented. Separate activation energies and frequency factors corresponding to independent and concurrent Arrhenius mechanisms are obtained from this procedure when the fluxes are of comparable magnitude. The method is developed in terms of membrane permeability theory since spatially separate and distinct diffusion pathways are of frequent occurrence in biological membranes. It is illustrated in the specific case of water diffusion through a keratin membrane. The results implicate the presence of “bound” water as a crucial factor in passive diffusion of water and polar molecules through the membrane.